Finally we set the limits of \(\mathring{H}^{(1)}\)  for the confluent Heun equation (CHE) which, in the form used by Arscott
[1]}, reads
\(x(x-1)\frac{d^2 S(x)}{dx^2}+[-\gamma +(\gamma +\delta )x+\rho x(x-1)]\frac{dS(x)}{dx}+(\alpha \rho x-\sigma )S(x)=0,\vspace{5.69054pt}\\\rho \ne 0,\quad (CHE),\nonumber \) 
